Answer:
Nick = 13 years old.
Step-by-step explanation:
Define the variables:
Given:
Create a system of equations with the given information and defined variables:
[tex]\begin{cases} w=n-5\\n+w=21\end{cases}[/tex]
Substitute the first equation into the second equation and solve for n:
[tex]\implies n+(n-5)=21[/tex]
[tex]\implies 2n-5=21[/tex]
[tex]\implies 2n-5+5=21+5[/tex]
[tex]\implies 2n=26[/tex]
[tex]\implies 2n \div 2=26 \div 2[/tex]
[tex]\implies n=13[/tex]
Therefore, Nick is 13 years old.
To find the age of Will, simply substitute the found value of n into the first equation and solve for w:
[tex]\implies w=13-5[/tex]
[tex]\implies w=8[/tex]
Therefore, Will is 8 years old.